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Brighi, L. and John, R., Characterizations of pseudomonotone maps and economic equilibrium, Journal of Statistics & Management Systems , Special Volume on Generalized Convexity, Generalized Monotonicity

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John, R. , Variational inequalities and pseudomonotone functions: some characterizations, Proceedings of the 5th Symposium on Generalized Convexity and Generalized Monotonicity , eds. J.-P. Crouzeix, J.-E. Martinez-Legaz and M. Volle, Luminy

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Abstract  

Let X ⊂ ℝ be an interval of positive length and define the set Δ = {(x, y) ∈ X × X | xy}. We give the solution of the equation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$F(G_1 (x,y),G_2 (u,v)) = G(F(x,u),F(y,v)),$$ \end{document}
which holds for all (x, y) ∈ Δ and (u, υ) ∈ Δ, where the functions F: XX, G 1: Δ → X, G 2: Δ → X, and G: F(X, X) × F(X, X) → X are continuous and strictly monotonic in each variable.

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Translational diffusion of poly-2,5-(1,3-phenylene)-1,3,4-oxadiazole (PMOD) in solution in 96% sulphuric acid was studied, and intrinsic viscosity was measured at different stages of thermal degradation. Polymer solution has previously been subjected to heating at temperature ranging from 75 to 104C and then investigated at 26C. A monotonic decrease in intrinsic viscosity and the molecular mass, M, of degraded products with increasing degradation temperature was detected. The rate constant of the degradation process has been obtained from the change in M of the degradation products with time at a fixed solution temperature, and the activation energy of the process was calculated by using the temperature dependence of the rate constant. The activation energy (E =1028 kJ–1 ) is close to that obtained previously for the hydrolysis of poly-2,5-(1,4-phenylene)-1,3,4-oxadiazole (PPOD) in sulphuric acid (106 kJ–1 ), the rate constant being approximately twice in the value.

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Abstract  

Let I ⊂ ℝ be an interval and κ, λ ∈ ℝ / {0, 1}, µ, ν ∈ (0, 1). We find all pairs (φ, ψ) of continuous and strictly monotonic functions mapping I into ℝ and satisfying the functional equation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\kappa x + (1 - \kappa )y = \lambda \phi ^{ - 1} (\mu \phi (x) + (1 - \mu )\phi (y)) + (1 - \lambda )\psi ^{ - 1} (\nu \psi (x) + (1 - \nu )\psi (y))$$ \end{document}
which generalizes the Matkowski-Sutô equation. The paper completes a research stemming in the theory of invariant means.

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Mixed-ligand chelate extraction of trivalent lanthanides such as La, Eu and Lu and a trivalent actinide, Am into xylene with mixtures of 1-phenyl-3-methyl-4-benzoyl-pyrazolone-5 (HPMBP) and dihexyl-N,N-diethylcarbamoylmethylphosphonate (CMP) has been studied by tracertechniques. These trivalent metal ions are found to be extracted from 0.01 mol/dm3 chloroacetate buffer solutions as M(PMBP)3·HPMBP type self adducts with HPMBP alone and in the presence of CMP as M(PMBP)3·CMP (where M=La, Eu, Lu and Am) into the organic phase. The equilibrium constants of the above species are deduced by non-linear regression analysis. The synergistic constants of trivalent lanthanides do not increase monotonically with atomic number but have a maximum at Eu and that of Am was found to lie between that of La and Eu.

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We offer a new framework for cellular automata modeling to describe and predict vegetation dynamics. The model can simulate community composition and spatial patterns by following a set of probabilistic rules generated from empirical data on plant neighborhood dynamics. Based on published data (Lippe et al. 1985), we apply the model to simulate Atlantic Heathland vegetation dynamics and compare the outcome with previous models described for the same site. Our results indicate reasonable agreement between simulated and real data and with previous models based on Markov chains or on mechanistic spatial simulation, and that spatial models may detect similar species dynamics given by non-spatial models. We found evidence that a directional vegetation dynamics may not correspond to a monotonic increase in community spatial organization. The model framework may as well be applied to other systems.

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Abstract  

New polyurethanes with mesogenic units in the main chain due to the use of a liquid crystalline chain extender were synthesized from 4,4'-methylenebis(cyclohexyl isocyanate) (HMDI)using diisocyanates of different trans, trans isomer content, a low molecular diol4,4'-bis(6-hydroxyhexoxy)biphenyl (BHHBP) and a high molecular poly(hexyleneadipate)diol (PHA). The growth of trans, trans isomer content in HMDI used to syntheses of PU induces monotonic growth of melting point, rectilinear growth of crystallization temperatures and the growth of crystallization enthalpy, both for hard segment polyurethanes and block polyurethanes. The increase of trans, trans isomer content in HMDI increases also glass transition temperatures and dynamic storage modulus of the polyurethanes.

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This paper is devoted to study the following Schrödinger-Poisson system {Δu+(λa(x)+b(x))u+K(x)ϕu=f(u),x3,Δϕ=4πK(x)u2,x3, where λ is a positive parameter, aC(R3,R+) has a bounded potential well Ω = a −1(0), bC(R3, R) is allowed to be sign-changing, KC(R3, R+) and fC(R, R). Without the monotonicity of f(t)=/|t|3 and the Ambrosetti-Rabinowitz type condition, we establish the existence and exponential decay of positive multi-bump solutions of the above system for λΛ¯, and obtain the concentration of a family of solutions as λ →+∞, where Λ¯>0 is determined by terms of a, b, K and f. Our results improve and generalize the ones obtained by C. O. Alves, M. B. Yang [3] and X. Zhang, S. W. Ma [38].

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Differential scanning calorimetry (DSC), thermogravimetric analysis (TG) and dynamic mechanical analysis (DMA) of the blends ofepoxy cresol novolac (ECN) resin toughened with liquid carboxy terminated butadiene-co-acrylonitrile (CTBN) rubber have been carried out. Exothermal heat of reaction (ΔH) due to crosslinking of the resin in presence of diaminodiphenyl methane(DDM, as amine hardener) showed a decreasing trend with increasing rubber concentration. Enhancements of thermal stability as well as lower percentage mass loss of the epoxy-rubber blends with increasing rubber concentration have been observed in TG. Dynamic mechanical properties reflected a monotonic decrease in the storage modulus (E′) with increasing rubber content in the blends. The loss modulus (E″) and the loss tangent(tanδ) values, however, showed an increasing trend with rise of the temperature up to a maximum (peak) followed by a gradual fall in both cases. Addition of 10 mass% of CTBN resulted maximum E″ and tanδ.

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